Spring 2007. CS 1050 B Constructing Proofs

Syllabus (to be updated during the course)

Topics
Dates
Reading
Course overview. Administrative stuff. Introduction.
01.09
Course rules.
Rosen textbook, Chapter 1, pp.1-43.
Direct and indirect proofs.
01.11
(1) Intro Lecture
from Berkeley Class,
(2) Intro Lecture
from MIT Class.
(3) Rosen textbook, pp. 1-43,63-66.
Proofs by contraposition and by contradiction. Proofs by cases.
01.16

Same as above,
Rosen textbook, Chapter 1, pp 75-90.
Existence proofs. Basics of induction.
01.18
(1) Berkeley Lectures,
(2) Rosen textbook, Chapter 4, pp 91-100, 263-279.
More on induction.
01.23
(1) Berkeley Lectures,
(2) Rosen textbook, Chapter 4, pp 263-279.
Strong induction. Induction and recursion: an algorithmic perspective.
01.25
(1) MIT Lectures,
(2) Rosen textbook, Chapter 4, pp 283-291.
Sort and search algorithms. Finding MIN and MAX in a list of elements.
01.30
More on sort and search algorithms. MergeSort.
02.01
Berkeley Lectures
Solving recurrences.
02.06
Review for Quiz 1.
02.08
Quiz 1.
02.13
Review of the solutions for Quiz 1. More on solving recurrences
02.15
Notes by Milena Mikhail 12345
Asymptotic notation: Big-O.
02.20
Rosen textbook, Chapter 3, pp.180-190.
Principles of counting. Choice, permutations, combinations.
02.22
Rosen textbook, Chapter 5, pp.335-344, 347-353,
355-360.
Binomial coefficients. Practice problems on counting.
02.27
Rosen textbook, Chapter 5, pp.363-368, 370-379.
Introduction to probability. Conditional probability.
03.01
Rosen textbook, Chapter 6, pp.393-398, 404-406.
Review for Quiz 2.
03.06
Quiz 2.
03.08
Rosen textbook, Chapter 6, pp. 417-423
Review of the solutions for Quiz 2. More on probabilities. Bayes' theorem.
03.13
Rosen textbook, Chapter 6, pp. 426-433
Random variables. Expectation.
03.15
Rosen textbook, Chapter 6, pp. 426-433
Spring break.    
Variance.
03.27

Rosen textbook, Chapter 6, pp. 434-439
Berkeley Lectures
Markov's inequality. Chebyshev's inequality.
03.29
  
Hash tables. Birthday paradox.
04.03
Rosen textbook, Chapter 6, pp. 409-411
UCSD Lectures
Basics of number theory. Euclid's GCD algorithm.
04.05

Rosen textbook, Chapter 3, pp. 201-205, 215-217,
219-229.

Primality testing.
04.10

Rosen textbook, Chapter 3, pp. 210-214, 237-240.
Berkeley Lectures1 Berkeley Lectures2
Extended GCD. Modulo inverse. Basics of cryptography.
04.12

Rosen textbook, Chapter 3, pp. 231-235, 241-244,
Berkeley Lectures
Review for Quiz 3.
04.17
Quiz 3.
04.19
Review of the solutions for Quiz 3.
04.24